Quantum modified Regge-Teitelboim cosmology

TL;DR

This paper develops a canonical quantization framework for a modified brane cosmology model based on the Regge-Teitelboim approach, revealing a quantum potential with an embryonic epoch and quantum nucleation driven by an effective cosmological constant.

Contribution

It introduces a quantization scheme for the modified geodetic brane cosmology, identifying constraints and a truncated Virasoro algebra, and analyzes the quantum potential and nucleation process.

Findings

Quantum potential indicates an embryonic epoch.

Quantum nucleation driven by an effective cosmological constant.

Constraints form a truncated Virasoro algebra.

Abstract

The canonical quantization of the modified geodetic brane cosmology which is implemented from the Regge-Teitelboim model and the trace of the extrinsic curvature of the brane trajectory, K, is developed. As a second-order derivative model, on the grounds of the Ostrogradski Hamiltonian method and the Dirac's scheme for constrained systems, we find suitable first- and second-class constraints which allow for a proper quantization. We also find that the first-class constraints obey a sort of truncated Virasoro algebra. The effective quantum potential emerging in our approach is exhaustively studied where it shows that an embryonic epoch is still present. The quantum nucleation is sketched where we observe that it is driven by an effective cosmological constant.